In the process for the dimerisation of ethylene to give but-1-ene by means of a homogeneous catalyst obtained by the interaction of a preformed mixture of an alkyl titanate and an ether with a compound of aluminium of the formula AlR.sub.3 or AlR.sub.2 H as described in U.S. Pat. Nos. 4,532,370 and 4,615,998, small amounts of solid polymer are formed, which are deposited on the surface of the reactor and the heat exchanger tubes and which are very harmful to good operation of the process as they reduce the rate of heat transfer effects and necessitate frequent derivatives of the reactor in order for them to be removed.